Basic Trope: A person is made immortal... And really enjoys it.
Straight: Rachel is made immortal, and considers it the best thing that ever happened to her.
Rachel throws a never-ending party specifically to show off how awesome she thinks being immortal is.
Rachel's immortality leaves her trapped in an inescapable And I Must Scream situation, but she still considers it a good thing.
Downplayed: Rachel admits an immortal life isn't always fine and dandy, but feels that overall she's better off for it.
Rachel is an optimistic person and why shouldn't she be? She's got literally all the time in the world and all the wonders and adventures it contains to look forward to. There's no Age Without Youth, and there is a community of similarly happy immortal people who won't die on you.
Rachel is a Genki Girl thrill seeker who regularly does incredibly stupid and dangerous stunts just because she can.
Zig Zagged: Rachel swings between living up her immortality and endless Wangsting about how much it sucks.
Averted: Rachel treats living forever like she treats living temporarily: time that has to be given purpose and meaning, not good or bad in and of itself.
Enforced: The writer finds wangsty immortals to be boring and hackneyed; "Really, in centuries of history they wouldn't find anything worth living for?"
"Wow, Rachel, becoming made immortal certainly perked you up."
"Time heals all wounds, and I've literally got all the time in the world."
Invoked: Rachel is deliberately chosen to be made immortal because the being that grants this boon knows that her innate sense of optimism and good cheer would enable her to cope with it easier than someone else.
Defied: Rachel fears becoming a giggling immortal with no concept of life, death, or time, so she purposely experiences everything life throws at her, good and bad, without flinching.
Discussed: "Immortality really is the best anti-depressant imaginable."
"I don't like to think what she'll be like after she sees her great grand children die. Not because it'll make her sad or callous, but because she'll be happy again in no time at all." "But that doesn't mean she doesn't still cherish their memories, just that she's eventually able to move on like any of us — what's she supposed to do, spent eternity wallowing in angst over the memories over people who died hundreds or thousands of years beforehand? Would they want her to live like that?"
Rachel's good cheer is a Stepford Smiler cover she uses to keep her sane; otherwise, the horror of living forever would drive her mad as she witnesses the death of all her loved ones, and is left lonely despite the the number of people she meets.
Rachel's attitude quickly changed once the downsides start kicking in. She eventually becomes confused and depressed when she finally realizes the mistake she has made.
Rachel is constantly forced to find new and creative ways to keep her spirits up and find ways to avoid boredom, is constantly skipping town and having to avoid any meaningful relationships, forcing her to only engage in wild flings and abandoning her family and friends.
Rachel only finds immortality fun because she's a narcissistic sociopath, has no loved ones and does not understand what all that fuss about them is, and finds amusement in her ability to escape consequences due to this. She has neither family nor friends, but mooks and sycophants instead, who are easily interchangeable.
Rachel's immortality brings dark patches, but on the whole she still manages to roll with the punches and for the most part enjoy her life.
Time heals all wounds, and Rachel has all the time in the world. Over the years, she learns how to deal with the downsides, and the immortality blues become just a part of the learning curve.
Rachel's family and friends are also immortal; they live with her and travel with her. Her neighbors envy the close relationship forged by their shared eternity.
Rachel only finds immortality fun because she's an All-Loving Hero, and finds fullfillment in her ability to help and inspire others to enjoy life. Alternatively, she's The Cape and works in emergency services (firefighters, coastguard, peacecorps, police, etc) because she can go into the most dangerous of situations and survive every time. By the time she's 500 she's saved enough lives to fill a moderate sized country.
Played For Laughs: Rachel spends her immortality on TV Tropes.